Gwent Police Chief Constable Pam Kelly has said the force has not yet issued any fines to people flouting social distancing legislation in the force area but warned that would change if people continued to ignore advice.
"I think it's fair to say that across Wales we've tried to get the balance right [on enforcement] from the word go," she told Radio Wales Breakfast.
"It's new legislation; some people are of course bearing in mind the 69 deaths across Wales and want us to be very hard, and some want us to work with the community."
She said Gwent wanted to "explain the situation and educate people" in these "unprecedented times".
"We've spoken to lots of people and we've been very visible," she said.
"As time unfolds we are becoming concerned that people are becoming complacent about what is an essential journey."
She said officers were explaining to people what was expected of them and asking them to return home.
However she added: "Make no bones about it, if people do not listen and breach the legislation, we will be fining.
"We will absolutely apply it if necessary, but I think that most people are seeing we have some of the toughest few weeks ahead of us and that complying with the legislation is the most important thing to do."
The chief constable also had a message for those looking to take criminal advantage of the current situation.
"Believe it or not, because the streets are so much quieter, the people that are out there intent on committing crime stand out so actually it's very easy for us to spot those people who are intent on causing havoc when we need calmness."